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What is the digit on the units place in the expanded value of 97^275 –
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04 Jul 2019, 01:48

For finding the unit digit of any number, cyclic digit of that number needs to be known.here, 7 has a cyclic rotation like 7, 9, 3, 1 2 has a cyclic rotation like 2, 4, 8, 6so, 97^275 must be ended in 3 and 32^44 must be ended in 6hence, the unit digit will be 7.so, the correct answer choice is (D)

This is the same as finding the units digit of 7ˆ275 - units digit of 2ˆ44;Number 7 has a cycle of 4 {7,9,3,1}, and Number 2, also, has a cycle of 4 {2,4,8,6};The units digit of 7ˆ275 will be the cycle number of the set equal to the remainder of 275/4, which is remainder 3, so its cycle num: 3;The units digit of 2ˆ44 will be the cycle number of the set equal to the remainder of 44/4, which is remainder 0, so its the last cycle num: 6;So, the units digit of 7ˆ275 - units digit of 2ˆ44 is equal to: 3 - 6 = -3, when we get a negative value, we subtract from 10, thus 10-3=7.

Answer (D).

PS: the cyclicality of a numbers units digit is given by that units digit raised to a power, for instance[1] has a cycle of 1, because 1ˆ1, 1ˆ2, 1ˆ3… will always return 1; [2] has a cycle of 4, because after 2 to an exponent divisible by 4 will always repeat the same units digit:2ˆ1=2 has a units of 2, 2ˆ2=4 has a units of 4, 2ˆ3=8 has a units of 8, 2ˆ4=16 has a units of 6,2ˆ5=32 has a units of 2 (here it begins to repeat the cycle).2ˆ6=64 has a units of 4 etc…[3] has a cycle of 4 {3,9,7,1}[4] has a cycle of 2 {4,6}[5] has a cycle of 1 {5}[6] has a cycle of 1 {6}[7] has a cycle of 4 {7,9,3,1}[8] has a cycle of 4 {8,4,2,6}[9] has a cycle of 2 {9,1}the end.

gmatclubot

What is the digit on the units place in the expanded value of 97^275 –
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05 Jul 2019, 12:57